A tree decomposition \(T=(V,E, (B_v)_{v \in V})\)  of
\(_0\)  of width at most \(2k+1\)  can be computed in time
\(2^{O(k)} \cdot |{adom}(_0)|\) [1]}. We may assume that \((V,E)\)  is a directed tree
by choosing a root \(v_0 \in V\) . For each \(v \in V\) , let \(_v\)  be
the restriction of database \(_0\)  to the constants that appear in
some bag \(B_u\) , \(u\)  a node in the subtree of \((V,E)\)  rooted at \(v\) .
Our aim is to traverse the tree \((V,E)\)  bottom-up, computing for each
\(v \in V\)  a representation of the models of the database \(_v\) 
and ontology , enriched with additional information about partial
homomorphisms from CQs in the UCQ \(q\)  to .
